Island freshwater lenses are often subjected to pumping to support the freshwater needs of isolated communities. Investigations of the lens extent commonly involve the application of analytical solutions, although the effects of pumping from circular island aquifers have not been assessed in previous analytical methodologies. In this study, a new analytical solution is derived based on Green's functions that accommodate freshwater inputs (recharge) and outputs (multiple wells) when obtaining the head distribution and sharp-interface lens shape. The solution is verified using a finite-element model for an illustrative pumping scenario. The solution is also differentiated with respect to pumping rates, recharge, and island radius to obtain vulnerability indices to characterize the lens sensitivity to changes in stresses. Finally, the analytical methodology is modified to examine the effects of non-uniform recharge. Python code incorporating the new solution is included to enable users to investigate a range of recharge and pumping scenarios.

中文翻译：

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确定补给有限的圆形岛屿中抽水淡水透镜体范围的分析方法

岛屿淡水透镜体经常需要抽水来满足偏远社区的淡水需求。尽管以前的分析方法尚未评估从圆形岛屿含水层抽水的影响，但对透镜体范围的研究通常涉及分析解决方案的应用。在这项研究中，基于格林函数导出了一种新的解析解，该函数在获得水头分布和锐界面透镜形状时适应淡水输入（补给）和输出（多井）。使用有限元模型针对说明性泵送场景验证了该解决方案。该解决方案还针对泵送速率、补给和岛屿半径进行区分，以获得脆弱性指数来表征透镜对应力变化的敏感性。最后，修改分析方法以检查不均匀补给的影响。包含包含新解决方案的 Python 代码，使用户能够研究一系列充电和泵送场景。